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COMPLETE

SECONDARY ALGEBRA

QUADRATICS AND BEYOND

COMPLETE

SECONDARY ALGEBRA

BY

GEORGE EGBERT FISHER, M.A., Ph.D.

AND

ISAAC J. SCHWATT, Ph.D.

ASSISTANT PROFESSORS OF MATHEMATICS IN THE

UNIVERSITY OF PENNSYLVANIA

QUADRATICS AND BEYOND

New York
THE MACMILLAN COMPANY

LONDON: MACMILLAN & CO., LTD.

1916

All rights reserved

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CHAPTER XVIII.

QUADRATIC EQUATIONS.

1. A Quadratic Equation is an equation of the second degree in the unknown number or numbers.

E.g., Q= 25, 2 – 5x + 6= 0, 2 + 2xy = 7.

A Complete Quadratic Equation, in one unknown number, is one which contains a term (or terms) in 2*, a term (or terms) in x, and a term (or terms) free from x, as 22 — 2 ax+b=cx—d.

A Pure Quadratic Equation is an incomplete quadratic equation which has no term in x, as aca 9= 0.

Pure Quadratic Equations.

2. Ex. 1. Solve the equation 6 – 7= 3.202 +5.

Transferring 3 22 to the first member, and 7 to the second member,

6 0 - 3 2 = 5+7,

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Dividing by 3,

2 = 4. The value of x is a number whose square is 4. But

22 = 4, and (-2)= 4. Therefore

X = +2.

3. This example illustrates the following principle of equivalent equations :

The positive square root of the first member of an equation may be equated in turn to the positive and to the negative square root of the second member.

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